# If You Rearrange The Letters Of Postmen

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## If You Rearrange The Letters Of Postmen

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Received: 31 May 2019 / Revised: 8 July 2019 / Accepted: 9 July 2019 / Published: 23 July 2019

When light from a distant source, such as a galaxy or a supernova, travels towards us, it is deflected by massive objects in its path. When the mass density of the distorted object exceeds a certain threshold, multiple, highly distorted images of the source are observed. This strong gravitational lensing effect has so far been treated as a model fitting problem. Using multiple observed images as constraints provides a self-contained model of the mass density inverted by the object source. When several models satisfy the constraints equally, we develop lens properties that separate data-based explanations from model assumptions. Multiple observed images allow us to determine the intrinsic properties of the perturbing mass distribution for any mass scale from a single simple set of equations. Their solution is unique and non-destructive model-based. The reconstruction of the source objects can be model-independent, allowing us to study galaxy evolution without the bias of the lensing model. Our approach reduces the lens and source information to its data-based evidence that all models agree on, facilitates the automated handling of large data sets, and allows the production of global information that is consistent with model-based information.

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Cosmology; dark matter; gravity lens; strength; techniques; analysis; clusters of galaxies; general; galaxy; mass work; techniques; data analysis; cosmology; distance scale cosmology; dark matter; gravity lens; strength; techniques; analysis; clusters of galaxies; total; galaxy; mass work; techniques; data analysis; cosmology; distance level

Forty years ago, in 1979, two images of the quasar QSO 0957+561 were seen, [1], which marked the discovery of strong gravitational lenses. The first description of the image configuration in the form of a lens model followed in [2]. In 1986, light arcs, highly magnified images of background galaxies, were discovered behind the galaxy clusters Abell 370 and Cl2244-02, [3, 4]. The first Abell 370 lens designs were presented in [5, 6]. Since then, multi-photon observations have been frequently used to study the skewed mass mass distribution, especially to infer its dark matter content and dark matter properties—see, e.g., [7, 8] for phase lensing observations. of the galaxy. , or [9, 10] for galaxy-scale lensing observations. Recent measurements with cluster-scale lensing simulations show that many different methods reconstruct the mass density distribution in the multi-image area enlarged to a few percent, [11]. For galaxy-scale lenses, a similar project is currently being pursued, [12]. Furthermore, the gravitational lensing of time-varying objects has been used as a cosmological probe to determine the Hubble-Lemaître constant,

, [13, 14, 15]. Attempts to investigate the spatial curvature of the universe, the density parameter of the universe, and the dark energy properties of the current cosmic structure and its possible extensions are also being pursued with galactic scale lenses and mergers, [16, 17, 18]. Even after forty years of intensive studies of gravitational lensing, it is still a subject of great research interest because of unprecedented observations, such as the supernova (SN) Refsdal, [19], or the recently discovered fast radio bursts ( FRBs), [20], has always contributed to the development of methods for further lens reconstruction and therefore to widen the range of applications of sharp lenses.

In our research, which continues in [21, 22, 23, 24, 25, 26, 27], we pursue the question which properties of a strong gravitational lens can be inferred directly from the observations that describe the multi-photon configuration. In contrast to many methods, we do not aim at the reconstruction of the global density of the whole lens which usually uses observables as constraints in the model fitting problem. For galaxy-scale lenses, reconstructions of such global lenses using parametric models or free-form methods can be found in [ 28 , 29 , 30 , 31 , 32 , 33 ], for example. Galaxy cluster densities can be reconstructed by global lensing reconstruction as, for example, described in [ 34 , 35 , 36 , 37 ]. References for more methods and comparisons between methods can be found in [11]. Some previously developed methods for galaxy-scale lenses can also be used and extended to reconstruct cluster-scale lenses and vice versa, see [38] for example. Because of the high symmetry of lenses on galactic scales, fully automatic characterizations are easier to implement than cluster scale lenses. The latter usually requires at least a visual inspection of the results, or manual corrections in intermediate steps. Furthermore, focusing on global properties, sparsely distributed multiple images are not sufficient to fully constrain the mass density within clusters, [39]. Therefore, different methods use different additional information and assumptions to reconstruct the mass-density distribution, which complicates the comparison of results.

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Instead of looking for a global invertible density that can lead to multiple observed images, we separate the data details from the underlying assumptions to find those lens properties that all methods agree on. We use the more general equations of the standard gravitational lensing mechanism to directly determine the properties of the inner lens from observations. These intrinsic properties are unique and calculated in the same way for all lenses from galactic scale lenses to amorphous galactic scale lenses. Therefore, the method is very efficient and robust to handle large datasets with minimal manual intervention.

The cosmic distance between us, the lens, and the source is usually determined according to the standard universe model and is, therefore, model-independent, see e.g., [40]. To make them independent of any assumptions about the origin and total abundance of dark matter and dark energy in the universe, we set the cosmic distance based on data from the recent Pantheon sample of type Ia SNe, [41]. This covers SNe up to redshift 2.3 so that data-dependent distances are available for most of the lensing configurations considered. In this way, our method does not rely on a specific lensing model and a specific extension of the background model of the universe, which is simply assumed to be spatial and isotropic and should satisfy Einstein’s field equations. To configure the data-based global distance, we use the standard analysis framework introduced in [42] for the efficiency of running time and numerical stability. Other methods of developing distance measures based on standard candles are, for example, [43, 44, 45, 46].

In this work, we summarize the current state of our method, we show a comparison with different ansatzes for global lens reconstruction, according to [47, 48], and in detail its contribution to determining the transformation of the invariance of the more general equations of gravitational lens mechanism. , especially the time delay equation that is used to estimate

. Based on these results, we outline the future development of lens reconstructions that can be activated and tested by the recently detected FRBs, as further described in [49].

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The next sections are organized as follows: In Section 2, we introduce the theory of independent lens identification for the setup of multi-image leading arrays. We list the internal lens properties that can be determined and seen differently in each multi-image configuration. Section 3 shows examples of these different cases at the galaxy and galaxy cluster scale and the results obtained with our method. We also estimate how accurate it is

Can be determined from a time delay equation that uses the angular radius distance based on the Pantheon data. After these proof-of-concept examples, we summarize the features and applications of our method in Section 4 and conclude the review with a graphical overview of our method.

In this section, we introduce theoretical concepts to determine the internal properties of a gravitational lens without assuming a specific lens model and without assuming the specific parameters of a spaceless and isotropic Friedmann cosmology. Many cases of